We present a picosecond supercontinuum light source designed for stroboscopic white-light interferometry. This source offers a potential for high-resolution characterization of vibrational fields in electromechanical components with frequencies up to the GHz range. The light source concept combines a gain-switched laser diode, the output of which is amplified in a two-stage fiber amplifier, with supercontinuum generation in a microstructured optical fiber. Implemented in our white-light interferometer setup, optical pulses with optimized spectral properties and below 310 ps duration are used for stroboscopic illumination at freely adjustable repetition rates. The performance of the source is demonstrated by characterizing the surface vibration field of a square-plate silicon MEMS resonator at 3.37 MHz. A minimum detectable vibration amplitude of less than 100 pm is reached.